How are grades calculated in Cirrus?

Grade calculation in Cirrus

In Cirrus, to assign grades to test scores, you choose an assessment scale. For example 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6  (1-10 (55%) – TIENDE cijfers - mét cijfers tussen 5 en 6). In this assessment scale, the percentage (here: 55%) is used to determine the cut-off score (fail/pass boundary). The grades are determined based on the cut-off score: grades 1-5.4 below the cut-off score and grades 5.5-10 from the cut-off score.

The default grade sequence set in Cirrus runs from 0-10. The various assessment scales in Cirrus use '1-10' because grades below 1 are not used. The grades 0-1 have been converted to 1.

Example:

• Assessment scale: 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6

• 40 multiple choice questions with 4 alternatives

• Maximum possible score: 40

• Cut-off score: 40*0.55= 22

The 5.5 (= lowest pass) is based on a percentage (here: 55%) of the maximum possible score (here: 40). The remaining grades are distributed upwards and downwards at equal intervals from the cut-off point.

• With test score 22, the student receives a grade 5.5

• If the test score is < 4.2, the student will receive a grade 1

The 40 score points are divided over 100 points (because of rounding off to 1 decimal: 0.1;0.2;0.3…9.9;10).

The number of score points divided over 55 grade steps below 5.5 (from 0 to 5.49) is 22 (22 - 0). The number of score points above the cut-off mark that is divided over 45 grade steps (from 5.5 to 10) is 18 (40-22). This gives the following score distribution.

In this distribution, the series actually starts with test score 0 = grade 0. Score 3.8 - 4.19 = grade 1. However, students with test scores below 4.20 all receive a grade 1.

Grade calculation in Cirrus when applying chance score correction

When constructed response questions are used in Cirrus, the option is given to apply chance score correction to determine the cut-off score. This is based on the chosen assessment scale. The formula used to calculate the cut-off score is:

((maximum possible score - chance score)* cut-off percentage) + chance score


The formula that Cirrus applies is a common formula for calculating the cut-off score with chance score correction. Note that this is not the same as calculating grades with a formula. Only the cut-off score is calculated with this formula. The grades above and below 5.5 are distributed in the same way as for the 'original' assessment scale from the cut-off point with equal intervals upwards and downwards. After the test has been administered and scored, the test scores are linked to the grades.


Example:

• Assessment scale: 1-10 (55%) 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6

• 40 mc questions with 4 alternatives

• Maximum possible score: 40

• Chance score: 40*0.25= 10

• Cut-off score: ((40-10)*0.55) + 10= 26.5

• With a score of 26.5, the student receives a grade 5.5

• If the score is < 13.15, the student will receive a grade 1


The 30 score points (40-10) are divided over 100 grade points (because of rounding to 1 decimal: 0.1;0.2;0.3….9.9;10). The number of score points divided over 55 grade steps below 5.5 (from 0 to 5.49) is 16.5 (26.5 - 10) and the number of score points above the cut-off point that is divided over 45 grade steps (from 5.5 to 10) is 13.5 (40-26.5). This gives the following score-grade distribution.

In this distribution, the series actually starts with test score 10 = grade 0. Score 12.85 to 13.14 = grade 1. However, students with test scores below 13.15 all receive a grade 1.

Grade calculation in Cirrus after changing the cut-off percentage

When setting the assessment scale in Cirrus, you can change the default cut-off percentage of '55%'. The cut-off score (pass/pass boundary) is then calculated based on the percentage entered. The other grades are based on the cut-off score: grades 1-5.4 below the cut-off score and grades 5.5-10 from the cut-off score.

After changing the cut-off percentage, the series of grades changes from 0-10 (where 0-1 = 1) to 1-10.

Example:

• Assessment scale: 1-10 (55%) 1-10 (55%) – rounded off to grades with decimals – with grades between 5 and 6

• 40 mc questions with 4 alternatives

• Maximum possible score: 40

• Cut-off score: 40*0.65= 26

• With test score 26, the student receives a grade 5.5

• If the test score is 0, the student will receive a grade 1

 

The 40 score points are divided over 90 grade points (grades from 1-10 and rounding of 1 decimal: 1.1;1.2;1.3…9.9;10).

The number of score points distributed over 45 grade steps below 5.5 (from 1 to 5.49) is 26 (26 - 0) and the number of score points above the cut-off point that is divided over 45 grade steps (from 5.5 to 10) is 14 (40-26). This gives the following score-grade distribution.

Because more score points are distributed under the cut-off score, the steps are larger than above the cut-off score. This gives a distribution with a kink at 5.5.

In this distribution, the series starts with test score 0 = grade 1.

If you want to use a cut-off percentage other than 55% in combination with grades from 0-10 (where 0-1 = 1),  you have to export the test scores from Cirrus and calculate the grades outside Cirrus. You can use a specially developed conversion file (Excel). See How do I modify the Cirrus results outside Cirrus and transfer them to Osiris? for more information. Please ask for help from your faculty’s digital assessment coordinator.